Replace the tag to fit the OP's intentions. Don't mark it as a synonym.
I do not think they should be merged. I think those three questions tagged as checksum should simply be edited to use hash instead. There is a very big difference between checksums and hashes. A hash is a stateless function that maps data of an arbitrary size to a fixed size in the form of ƒ : {0,1}* → {0,1}n. A checksum on the other hand is typically nothing more than the weighted summation of a function of each data word (whether said function is a lookup table or the identity function), modulo a small value. This is a very specific definition and does not at all apply to hashes. If only three people are using the tags, just replace it, don't merge it.
I've went ahead and made the edits since this answer has been the most upvoted for the past 18 days. If I went ahead too soon, feel free to revert the edits for more discussion.